In this section, students learn about odd and even numbers, building on their experience with sharing objects with another person or with making pairs out of a set of objects. They begin by noticing that some groups of objects can be made into two equal groups without a “leftover” and other groups can be made into two equal groups with “1 leftover.” The same pattern can be seen when pairing objects.

After learning the terms “even” and “odd,” students focus on explaining why a group has an even number or an odd number of members. They do so by showing whether the objects can be made into 2 equal groups or paired without any leftover objects, or whether they can skip-count by 2 to count the entire collection.

The representations used here support students as they progress from explaining even and odd numbers informally to doing so more formally. They also pave the way for students to make sense of representations of multiplication in grade 3.

Early lessons of this unit encourage the teacher to record student thinking using diagrams of equal groups or by arranging objects in rows and columns. Both of these recording strategies help students see and count pairs of objects.

Students begin to see how objects arranged in rows and columns can show equal groups or pairs. They will learn more about this arrangement and the term “array” in the next section.

To focus the work on building a foundation for multiplication and division, counters or connecting cubes should be available to students throughout the section, including during Cool-downs.

In this section, students learn that a rectangular array contains objects arranged into rows and columns, with the same number of objects in each row and the same in number of objects in each column.

Using this structure, students can skip-count by the number in each row or in each column to find the total number of objects. They can also write equations with equal addends representing the number of objects in a row or a column.

Later in the section, students relate their work with arrays to the partitioning of shapes into equal parts.

True or false?

True or false?

Students build rectangles by arranging square tiles into rows and columns, and then partition rectangles into rows and columns.

Use 8 tiles to build a rectangle. Arrange them in 2 rows.

Partition this rectangle to match the rectangle you made.

Rectangles in this section have up to 5 rows and 5 columns. Students are not expected to name the fractional units created by partitioning shapes. The focus is on using the structure of the rows and columns created by the partitions to count the total number of equal-size squares. This work serves as a foundation for students’ future study of multiplication and area measurement.